I've never been on a 4nt, only 3nt (12 years ago) and 7nt--is there a formal and/or semi formal night on the 4nt?
Some family members went on a 3nt in December and I told them how we generally dress for the formal and semi formal nights, but they decided to be more casual--the men wore l/s oxfords with dress khakis and the women wore sundresses and maxi dresses and they all said they felt under dressed. YMMV.
In my family of five, we like to get dressed up a few times a year, so we definitely take advantage of it on the cruise. My oldest (13) will wear a suit and tie, my 7yo will wear dress pants with a jacket, dress shirt, and tie. I'll try to wrestle my 3yo into a "fancy" dress. I don't think that younger kids need to be in tuxes, although my husband will be and I know that other people put their children in tuxes.